(5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant. Show that T is a scalar multiple of the identity operator.
(5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant. Show that T is a scalar multiple of the identity operator.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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q5
Transcribed Image Text:(5) Suppose that \( T \in \mathcal{L}(V) \) is such that all subspaces of \( V \) of dimension \( \text{dim}(V) - 1 \) are \( T \)-invariant. Show that \( T \) is a scalar multiple of the identity operator.
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